A. G. W. Cameron’s research while affiliated with Yeshiva University and other places

There has been discussion in the literature as to whether the cumulative number of levels in light nuclei varies more nearly as exp(const. ) or exp(const. E), where E is the excitation energy. The question is examined in this paper. It is found that if one constructs "step diagrams" by plotting the cumulative number versus the energy, both formulas represent the data almost equally well. However, additional consideration of levels counted above neutron and proton binding energies shows that exp(const. ) fails badly to represent the data, whereas exp(const. E) continues to give good fits. In either case E may be measured above an arbitrary ground-state energy E0. If the satisfactory formula is written in the form exp(E–E0)/T, then it is found that the dependence of the slope on mass number may be expressed in approximately the form T−1 = 0.0165A MeV−1, but there are significant deviations from this relation apparently related to shell structure. The intercepts E0 are quite variable but are roughly clustered according to the oddness or evenness of the neutron and proton numbers of the nucleus.

A new mass formula has been constructed which contains volume and surface energies, each with a symmetry energy contribution, Coulomb and Coulomb exchange energies, and shell correction and pairing energies. A nuclear model with a trapezoidal radial-density distribution was used. The central density was assumed constant, and the dimensions were adjusted to fit the Stanford electron-scattering results. The symmetry energy coefficients were determined by a least-squares fit to the valley of beta stability. The volume and surface energy coefficients were determined by a least-squares fit to 89 odd–odd masses uniformly spaced in mass number. The shell correction and pairing energies were assumed to be independent functions of the proton and neutron numbers; they were empirically determined from the differences between masses computed from the formula without corrections and those tabulated by Wapstra and Huizenga. The median energy difference between the corrected formula and the Wapstra–Huizenga masses is about 300 kev. Some remarks are made concerning the implication of these results for nuclear deformations and fission thresholds.

Various properties of dense matter in nuclear statistical equilibrium are studied for densities and temperatures in the range and . With increasing density the stability shifts to more and more neutron-rich nuclei. With increasing temperature the general tendency is that nuclei of smaller charge become more abundant, and the abundances of nuclei near a peak tend to become nearly as large as that of the peak nucleus. The shifting of the most stable region with change of density or temperature takes place rather abruptly from one neutron closed shell region to the next. For densities , the ordinary iron group nuclei are most stable until the temperature becomes about 5 × 109 °K; for higher temperatures matter in equilibrium consists of almost pure helium. For higher density, this transition to a helium phase takes place at a somewhat higher temperature, and the equilibrium configuration for temperatures below the helium transition point shifts to the neutron-rich side of the valley of beta stability. When , matter consists of almost pure neutrons at all densities. Rates of beta reactions and neutrino emission generally increase with increase of density and temperature. At a typical temperature of about 5 × 109 °K, the neutrino energy emission rate increases from about 2 × 1011 ergs/g sec at ρ ~ 106 g/cm3 to about 2 × 1017 erg/g sec at ρ ~ 3 × 1011 g/cm3.

Cameron has interpreted the heavy uranium mass yield curve from the Mike thermonuclear explosion as indicating that conventional atomic mass formulas do not give realistic values of neutron binding energies for neutron-rich nuclei off the valley of beta stability. In this paper two mass formulas are constructed which differ in the treatment of the nuclear symmetry energy. In one, essentially of conventional form, very neutron-rich nuclei become unbound. In the other, of a modified "exponential" form, very neutron-rich nuclei remain slightly bound. The three adjustable coefficients in each formula were determined by least-squares fits to the measured masses near the valley of beta stability; the formulas fit these masses about equally well with nearly the same values of the coefficients. Additional shell and pairing corrections were determined empirically. These corrections suggest a preference for the exponential formula. Some astrophysical applications of these results are qualitatively discussed.

Evolutionary sequences of solar models have been calculated using the Henyey method of model construction. These sequences were started at the threshold of stability, at which the released gravitational potential energy of the sun is just sufficient to supply the thermal, dissociation, and ionization energies of the model. It was found that the present solar characteristics were closely reproduced when a mixing length equal to two pressure scale heights was used in the convection theory, and when a solar initial helium abundance, based on solar cosmic-ray measurements, was chosen. The sun was again found to have a high luminosity during its contraction phase and to approach the main sequence in only a few million years. Tables of selected characteristics of some of the models are presented.

A normal solar abundance distribution of the elements was subjected to a calculated bombardment by protons and alpha particles having energy spectra of the form E−n, where n was usually taken to be equal to 2.5, and having low-energy cutoffs on the spectra at 1 MeV. Bombardment with protons resulted in breakdown of nuclei to lower mass numbers. Bombardment with alpha particles resulted in buildup of nuclei to higher mass numbers. It is concluded that preferential acceleration of alpha particles to varying total fluxes can produce the abundance anomalies of peculiar A stars in concentrated patches on the surface. Local surface magnetic fields in the range 106–107 G are required to provide the necessary energy sources for the accelerated particles.

A method is outlined by which thermonuclear reaction rates can be determined from the statistical properties of nuclei. Assuming that the contribution to the cross section of a given resonance is given by the Breit–Wigner single-level formula, the total rate is determined by integrating the product of the cross section, weighted by the nuclear level density, and the velocity over energy. The nuclear radiation widths were calculated on the assumption that electric-dipole transitions are dominant. The particle widths were determined by approximating the nuclear strength function by that value calculated for a black nucleus. Nuclear cross sections calculated in this manner are compared with experiment both for charged-particle reactions on lighter nuclei and for neutron-capture reactions proceeding on nuclei in the mass range A > 60. Good agreement is obtained in both cases.

It is usually assumed in modern theories of nucleosynthesis that the initial composition of the galaxy was pure hydrogen. The large solar and stellar content of helium has appeared to present a difficulty for such an assumption. This paper examines the problem. Numerical studies are made of the time changes in the compositions of stars and the interstellar medium as a result of stellar evolution. It is concluded that the large helium content of the sun and recently formed stars can be produced only as a result of the evolution of stars of approximately solar mass. Hence the initial hydrogen hypothesis requires a large age for the galaxy ( years). The content of long-lived radioactivities in the interstellar medium is also followed as a function of time. It is found that the ratios of radioactivities are very insensitive functions of time and are approximately those observed in the solar system when the helium content is satisfactory. However, it is also concluded that these ratios give little useful information about cosmochronology.

Two composite equations of state have been used in the investigation of the structure of neutron (or hyperon or baryon) stars. These have been based upon two forms of the neutron–neutron potential suggested by Levinger and Simmons. In one form, repulsive forces come in quickly at greater than nuclear densities, while, in the other form, the repulsive forces come in slowly. In the former case the maximum stable mass of a neutron star is about two solar masses, whereas in the latter case it is only about one solar mass. This probably represents a measure of the basic uncertainty in the properties of neutron-star models due to our lack of knowledge of nuclear forces. The maximum central density of a stable configuration is similarly uncertain; this density probably lies in the range 1015 to 1016 g/cm3. Details of many of the neutron-star models calculated are summarized and discussed.

Previous work by Gilbert and Cameron has demonstrated a linear relation between the nuclear level density parameter a and the mass shell correction S. However, different relations were obtained for deformed and undeformed nuclei. We show that a single relation can be obtained if a deformation energy is added to the reference mass formula. This deformation energy is shown to be proportional to the number of neutrons or protons to the nearest closed shell.